Please check these useful links.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3602368/

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4841590/

https://www.researchgate.net/publication/282618969_Multi-scale_network_analysis_shows_scale-dependency_of_significance_of_individual_protected_areas_for_connectivity

Article Multi-scale network analysis shows scale-dependency of signi...

Dear Jessica

I guess the software Conefor is the most appropriate tool to evaluating changes in connectivity under different management scenarios, by joining information about patch attributes (e.g. suitability) and isolation (e.g. Euclidean or ecological distance).

http://www.conefor.org/

I will follow you

Dear Jessica, 

i agree that Conefor is an excellent option to obtain connectivity index under different scenarios of anthropic action or climate change.

http://www.conefor.org

All the best,

Cris

Dear Jessica:

Hanski’s (1994 J Anim Ecol; see also Moilanen & Nieminen 2002 Ecology) connectivity index I4 seems highly relevant for your purpose. It can be easily computed as:

Ii =  Σi≠j exp(–αdij) × Sja

where:

dij is the distance between a given patch (i) and any other patch in the system (j),

Sj is the (other) patch area,

α is the parameter defining the dispersal kernel, reflecting the probability that individuals reach a certain distance, and so it is needed to ‘scale’ the formula (because, e.g. 1 km isolation distance may be nothing for birds, but a serious isolation for snails). In the case of the negative exponential function (NEF*) α can be approximated as 1/avg. dispersal distance, which for most temperate zone butterflies is several hundred meter to 1 km (so α value between 1 and let say 3 seems appropriate).

*You may actually consider a different kernel than the negative exponential one, e.g. inverse power function (IPF) - see e.g. Hovestadt et al. 2011 for the discussion, but NEF appears suitable in the case of butterflies.

a is the parameter defining the density-area relationship, and for butterflies I would assume that it is less than 1, i.e. the population size increase is less than proportional with increasing patch area, because smaller patch typically have higher population densities. Something between 0.67 and 0.75 seems reasonable (cf. Nowicki et al. 2007 Biol Conserv).

Since you have habitat suitability values (H) for each patch, I would replace Sja with Sj × Hj , because the habitat suitability is likely to account for population density, or perhaps even with just Hj if your suitability values already include patch sizes - it is unclear from your description if they are based merely on habitat type (or related characteristics) or also on patch size.

I hope the above explanation helps a bit.

Piotr

Conefor Sensinode is specially designed for connectivity metrics, is simple to use and gives you easy reading results. www.conefor.org/

Fragstats also has a couple of connectivity metrics at class and landscape level. http://www.umass.edu/landeco/research/fragstats/documents/Metrics/Metrics%20TOC.htm

Thank you for your answers. I think that Hanski's connectivity index is the most appropriate for my study, but I wonder how to calculate it in practice (this index is not implemented in Conefor, is it?)

Well, the formula is simple enough to be applied e.g. in Excel - see the attached example, in which I have demonstrated the calculations in step-by-step manner.

Greetings,

Piotr

PS. What butterfly is going to be your model species? I am working with butterflies as well, and thus I may be highly interested in the outcome of your study.

Since I'm working at high resolution in a very fragmented landscape, and I want to take into account all the range of habitat suitability values, I have more than a million of micro-patches and it is too heavy to be done in Excel. So I was wondering if there was an existing automated procedure that I could apply, otherwise I will try to code it in Python...

I'm working on the violet copper (Lycaena helle), and you?

Hi Jessica,  Many, many options here.   Colleagues and I recently published a paper on the issue of selecting metrics like those you're talking about. 

https://www.researchgate.net/publication/303847545_A_management-oriented_framework_for_selecting_metrics_used_to_assess_habitat-_and_path-specific_quality_in_spatially_structured_populations

Article A management-oriented framework for selecting metrics used t...

I agree to the above recommending Conefor sensinode. This could be the best option at large spatial scales. You can include commands to include/exclude new patches over time and check how they impact your connectivity estimates.

If trying to work at smaller spatial scales, then I would follow the classical Hansky connectivity formula as suggested by Piotr.

best luck

I wholly identify and flow with the proponents of the Conefor software for your analysis. If after, the result fails to satisfy your research objectives, you may try Hanski connectivity index. I am currently working on Protected Area network connectivity in the Niger Delta region of Nigeria and I am using Conefor software. Why not give it a try.